document.write( "Question 891981: Hi, this is my second time asking a question....both were on logarithms :(\r
\n" ); document.write( "\n" ); document.write( "Solve for x.
\n" ); document.write( "\"+log%28+2%2C+x%2B1+%29+\" = \"+log%28+4%2C+x%2B3+%29+\"\r
\n" ); document.write( "\n" ); document.write( "Because \"+log%28+4%2C+x%2B3+%29+\" can be rewritten as \"+%281%2F2%29log%28+2%2C+x%2B3+%29+\",
\n" ); document.write( "it was \"+log%28+2%2C+x%2B1+%29+\" = \"+%281%2F2%29log%28+2%2C+x%2B3+%29+\". Then,\r
\n" ); document.write( "\n" ); document.write( "\"+log%28+2%2C+x%2B1+%29+\" = \"+log%28+2%2C+%28x%2B3%29%5E%281%2F2%29+%29+\"\r
\n" ); document.write( "\n" ); document.write( "Thus, \"+log%28+2%2C+%28x%2B1%29%2Fsqrt%28x%2B3%29+%29+\" \r
\n" ); document.write( "\n" ); document.write( "But I don't know what to do next. Or did I do wrong from the beginning?\r
\n" ); document.write( "\n" ); document.write( "I know there could be another way... for example... making \"+log%28+4%2C+x%2B3+%29+\" = \"+log%28+10%2C+x%2B3+%29%2Flog%28+10%2C+4+%29+\" to make the same base for both sides. But still, I don't know what to do next.\r
\n" ); document.write( "\n" ); document.write( "Could you please teach me how to solve this problem in those two ways?
\n" ); document.write( "

Algebra.Com's Answer #540216 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
Hi, this is my second time asking a question....both were on logarithms :(\r
\n" ); document.write( "\n" ); document.write( "Solve for x.
\n" ); document.write( "\"+log%28+2%2C+x%2B1+%29+\" = \"+log%28+4%2C+x%2B3+%29+\"\r
\n" ); document.write( "\n" ); document.write( "Because \"+log%28+4%2C+x%2B3+%29+\" can be rewritten as \"+%281%2F2%29log%28+2%2C+x%2B3+%29+\",
\n" ); document.write( "it was \"+log%28+2%2C+x%2B1+%29+\" = \"+%281%2F2%29log%28+2%2C+x%2B3+%29+\". Then,\r
\n" ); document.write( "\n" ); document.write( "\"+log%28+2%2C+x%2B1+%29+\" = \"+log%28+2%2C+%28x%2B3%29%5E%281%2F2%29+%29+\"\r
\n" ); document.write( "\n" ); document.write( "Thus, \"+log%28+2%2C+%28x%2B1%29%2Fsqrt%28x%2B3%29+%29+\" \r
\n" ); document.write( "\n" ); document.write( "But I don't know what to do next. Or did I do wrong from the beginning?\r
\n" ); document.write( "\n" ); document.write( "I know there could be another way... for example... making \"+log%28+4%2C+x%2B3+%29+\" = \"+log%28+10%2C+x%2B3+%29%2Flog%28+10%2C+4+%29+\" to make the same base for both sides. But still, I don't know what to do next.\r
\n" ); document.write( "\n" ); document.write( "Could you please teach me how to solve this problem in those two ways?
\n" ); document.write( "

\n" ); document.write( "\"log+%282%2C+x+%2B+1%29+=+log+%284%2C+x+%2B+3%29\"
\n" ); document.write( "\"log+%282%2C+x+%2B+1%29+=+log+%28%28x+%2B+3%29%29%2Flog+4\" ------ Applying change of base
\n" ); document.write( "\"log+%282%2C+x+%2B+1%29+=+%28log+%282%2C+%28x+%2B+3%29%29%29%2Flog+%282%2C+4%29\" ----- Changing base on right to base 2
\n" ); document.write( "\"log+%282%2C+x+%2B+1%29+=+%28log+%282%2C+x+%2B+3%29%29%2F2\"
\n" ); document.write( "\"2log+%282%2C+%28x+%2B+1%29%29+=+log+%282%2C+x+%2B+3%29\" ------- Cross-multiplying
\n" ); document.write( "\"log+%282%2C+%28x+%2B+1%29%5E2%29+=+log+%282%2C+x+%2B+3%29\"
\n" ); document.write( "\"%28x+%2B+1%29%5E2+=+x+%2B+3\"
\n" ); document.write( "\"x%5E2+%2B+2x+%2B+1+=+x+%2B+3\"
\n" ); document.write( "\"x%5E2+%2B+2x+-+x+%2B+1+-+3+=+0\"
\n" ); document.write( "\"x%5E2+%2B+x+-+2+=+0\"
\n" ); document.write( "(x - 1)(x + 2) = 0
\n" ); document.write( "\"highlight_green%28highlight_green%28x+=+1%29%29\" OR x = - 2 (ignore)\r
\n" ); document.write( "\n" ); document.write( "After you'd obtained, \"+log%28+2%2C+x%2B1+%29+\" = \"+log%28+2%2C+%28x%2B3%29%5E%281%2F2%29+%29+\", you should have had: \"x+%2B+1+=+%28x+%2B+3%29%5E%281%2F2%29\", which is
\n" ); document.write( "the same as: \"x+%2B+1+=+sqrt%28x+%2B+3%29\"
\n" ); document.write( "\"%28x+%2B+1%29%5E2+=+x+%2B+3\" ------- Squaring both sides
\n" ); document.write( "Go on to solve for x. \n" ); document.write( "
\n" );